Grid Moment Maximization by Mathematical Programming

A plane grid representation of a highway bridge is analyzed for maximum moment under a moving load using the influence surface method. The ordinates of the influence surface are found at grid nodes (where stringers and diaphragms intersect) by use of a structural analysis program. These ordinates and the slopes at these points are used to determine in a manner similar to one used in finite element analysis of plates, an analytical expression of the whole surface. The grid is acted upon by a simple H20 loading. The sum of the products of the wheel loads and the ordinates of the influence surface at their locations defines an objective function. This objective function is a function of the position of the truck on the bridge; a mathematical programming procedure determines that position which causes the objective function to take on its maximum. A computer program automates the optimization. This program may be adapted to more general conditions, such as the skew bridge and multiple trucks, with or without variable axle spacing.